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- La ecuación:
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Ecuación x=(x+1)/2
- Ecuación (x-6)(-5x-9)=0
-
Ecuación x^2-14*x+33=0
-
Ecuación 5-x^2=0
- Expresar {x} en función de y en la ecuación:
- 12*x+1*y=15
- -17*x-12*y=-9
- 18*x+17*y=-14
- 14*x-10*y=-4
- Suma de la serie:
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0,8
-
Expresiones idénticas
- (5x- uno)(2x+ uno)-1 cero x2=0, ocho
- (5x menos 1)(2x más 1) menos 10x2 es igual a 0,8
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- 5x-12x+1-10x2=0,8
- (5x-1)(2x+1)-10x2=O,8
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Expresiones semejantes
- (5x+1)(2x+1)-10x2=0,8
- (5x-1)(2x+1)+10x2=0,8
- (5x-1)(2x-1)-10x2=0,8
(5x-1)(2x+1)-10x2=0,8 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
(5*x - 1)*(2*x + 1) - 10*x2 = 4/5
$$- 10 x_{2} + \left(2 x + 1\right) \left(5 x - 1\right) = \frac{4}{5}$$
Solución detallada
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$- 10 x_{2} + \left(2 x + 1\right) \left(5 x - 1\right) = \frac{4}{5}$$
en
$$\left(- 10 x_{2} + \left(2 x + 1\right) \left(5 x - 1\right)\right) - \frac{4}{5} = 0$$
Abramos la expresión en la ecuación
$$\left(- 10 x_{2} + \left(2 x + 1\right) \left(5 x - 1\right)\right) - \frac{4}{5} = 0$$
Obtenemos la ecuación cuadrática
$$10 x^{2} + 3 x - 10 x_{2} - \frac{9}{5} = 0$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 10$$
$$b = 3$$
$$c = - 10 x_{2} - \frac{9}{5}$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{\sqrt{400 x_{2} + 81}}{20} - \frac{3}{20}$$
$$x_{2} = - \frac{\sqrt{400 x_{2} + 81}}{20} - \frac{3}{20}$$
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$- 10 x_{2} + \left(2 x + 1\right) \left(5 x - 1\right) = \frac{4}{5}$$
en
$$\left(- 10 x_{2} + \left(2 x + 1\right) \left(5 x - 1\right)\right) - \frac{4}{5} = 0$$
Abramos la expresión en la ecuación
$$\left(- 10 x_{2} + \left(2 x + 1\right) \left(5 x - 1\right)\right) - \frac{4}{5} = 0$$
Obtenemos la ecuación cuadrática
$$10 x^{2} + 3 x - 10 x_{2} - \frac{9}{5} = 0$$
Es la ecuación de la forma
a*x^2 + b*x + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 10$$
$$b = 3$$
$$c = - 10 x_{2} - \frac{9}{5}$$
, entonces
D = b^2 - 4 * a * c =
(3)^2 - 4 * (10) * (-9/5 - 10*x2) = 81 + 400*x2
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{\sqrt{400 x_{2} + 81}}{20} - \frac{3}{20}$$
$$x_{2} = - \frac{\sqrt{400 x_{2} + 81}}{20} - \frac{3}{20}$$
Gráfica
Suma y producto de raíces
[src]
suma
_____________________________________ _____________________________________ _____________________________________ _____________________________________
4 / 2 2 /atan2(400*im(x2), 81 + 400*re(x2))\ 4 / 2 2 /atan2(400*im(x2), 81 + 400*re(x2))\ 4 / 2 2 /atan2(400*im(x2), 81 + 400*re(x2))\ 4 / 2 2 /atan2(400*im(x2), 81 + 400*re(x2))\
\/ (81 + 400*re(x2)) + 160000*im (x2) *cos|----------------------------------| I*\/ (81 + 400*re(x2)) + 160000*im (x2) *sin|----------------------------------| \/ (81 + 400*re(x2)) + 160000*im (x2) *cos|----------------------------------| I*\/ (81 + 400*re(x2)) + 160000*im (x2) *sin|----------------------------------|
3 \ 2 / \ 2 / 3 \ 2 / \ 2 /
- -- - -------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------- + - -- + -------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------
20 20 20 20 20 20
$$\left(- \frac{i \sqrt[4]{\left(400 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 160000 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(400 \operatorname{im}{\left(x_{2}\right)},400 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{20} - \frac{\sqrt[4]{\left(400 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 160000 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(400 \operatorname{im}{\left(x_{2}\right)},400 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{20} - \frac{3}{20}\right) + \left(\frac{i \sqrt[4]{\left(400 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 160000 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(400 \operatorname{im}{\left(x_{2}\right)},400 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{20} + \frac{\sqrt[4]{\left(400 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 160000 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(400 \operatorname{im}{\left(x_{2}\right)},400 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{20} - \frac{3}{20}\right)$$
=
-3/10
$$- \frac{3}{10}$$
producto
/ _____________________________________ _____________________________________ \ / _____________________________________ _____________________________________ \ | 4 / 2 2 /atan2(400*im(x2), 81 + 400*re(x2))\ 4 / 2 2 /atan2(400*im(x2), 81 + 400*re(x2))\| | 4 / 2 2 /atan2(400*im(x2), 81 + 400*re(x2))\ 4 / 2 2 /atan2(400*im(x2), 81 + 400*re(x2))\| | \/ (81 + 400*re(x2)) + 160000*im (x2) *cos|----------------------------------| I*\/ (81 + 400*re(x2)) + 160000*im (x2) *sin|----------------------------------|| | \/ (81 + 400*re(x2)) + 160000*im (x2) *cos|----------------------------------| I*\/ (81 + 400*re(x2)) + 160000*im (x2) *sin|----------------------------------|| | 3 \ 2 / \ 2 /| | 3 \ 2 / \ 2 /| |- -- - -------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------|*|- -- + -------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------| \ 20 20 20 / \ 20 20 20 /
$$\left(- \frac{i \sqrt[4]{\left(400 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 160000 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(400 \operatorname{im}{\left(x_{2}\right)},400 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{20} - \frac{\sqrt[4]{\left(400 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 160000 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(400 \operatorname{im}{\left(x_{2}\right)},400 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{20} - \frac{3}{20}\right) \left(\frac{i \sqrt[4]{\left(400 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 160000 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(400 \operatorname{im}{\left(x_{2}\right)},400 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{20} + \frac{\sqrt[4]{\left(400 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 160000 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(400 \operatorname{im}{\left(x_{2}\right)},400 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{20} - \frac{3}{20}\right)$$
=
-9/50 - re(x2) - I*im(x2)
$$- \operatorname{re}{\left(x_{2}\right)} - i \operatorname{im}{\left(x_{2}\right)} - \frac{9}{50}$$
-9/50 - re(x2) - i*im(x2)
Respuesta rápida
[src]
_____________________________________ _____________________________________
4 / 2 2 /atan2(400*im(x2), 81 + 400*re(x2))\ 4 / 2 2 /atan2(400*im(x2), 81 + 400*re(x2))\
\/ (81 + 400*re(x2)) + 160000*im (x2) *cos|----------------------------------| I*\/ (81 + 400*re(x2)) + 160000*im (x2) *sin|----------------------------------|
3 \ 2 / \ 2 /
x1 = - -- - -------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------
20 20 20
$$x_{1} = - \frac{i \sqrt[4]{\left(400 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 160000 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(400 \operatorname{im}{\left(x_{2}\right)},400 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{20} - \frac{\sqrt[4]{\left(400 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 160000 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(400 \operatorname{im}{\left(x_{2}\right)},400 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{20} - \frac{3}{20}$$
_____________________________________ _____________________________________
4 / 2 2 /atan2(400*im(x2), 81 + 400*re(x2))\ 4 / 2 2 /atan2(400*im(x2), 81 + 400*re(x2))\
\/ (81 + 400*re(x2)) + 160000*im (x2) *cos|----------------------------------| I*\/ (81 + 400*re(x2)) + 160000*im (x2) *sin|----------------------------------|
3 \ 2 / \ 2 /
x2 = - -- + -------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------
20 20 20
$$x_{2} = \frac{i \sqrt[4]{\left(400 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 160000 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(400 \operatorname{im}{\left(x_{2}\right)},400 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{20} + \frac{\sqrt[4]{\left(400 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 160000 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(400 \operatorname{im}{\left(x_{2}\right)},400 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{20} - \frac{3}{20}$$
x2 = i*((400*re(x2) + 81)^2 + 160000*im(x2)^2)^(1/4)*sin(atan2(400*im(x2, 400*re(x2) + 81)/2)/20 + ((400*re(x2) + 81)^2 + 160000*im(x2)^2)^(1/4)*cos(atan2(400*im(x2), 400*re(x2) + 81)/2)/20 - 3/20)